Once the indices are calculated the job is done and all tile edges and corners should (in theory) match up !!

Not too sure I follow your 5_95_0_7 arrangement. This is the bottom left of a fixed tilemap layout. But see the explanation here (at my cr31 site) for generating random 'Blob' layouts by either Method 1 or Method 2.

The large random layout image is actually generated by a third Method 3. A simple orthogonal (no diagonals) maze is created and as the path progresses, rooms (or islands) are filled in. This ensures all rooms are connected. See here (bottom of page) for a fuller explanation.

An advantage of maze generation is that it can be adjusted to create a few long winding or many short stubby paths leading to different balance of rooms, paths and general meandering. You can try it out here. Choose a Blob tileset and then click on 'Maze' (instead of 'Random') and watch it go to work. Mazes can be any size but the outer stage edge is always 0. Also the generator never merges paths together (perfect maze only) so there is always one unique path between any two tiles. I might add in some further controls to allow for path merging. Hope the links help. I'll tidy up some cr31 texts to make things clearer. Let me know if you need more info. Thanks, Guy.

I've drawn them out to better appreciate their beauty and (almost) perfect symmetry. It's the 'almost' that drives you potty when trying to find such layouts by hand.

So, a puzzle of 46 shaped pieces could be formed into a single connected island. Maybe into the 7 by 7 lid of the box the puzzle came in. A perfect Blob island.

Many thanks Caeles for your exhaustive searches and no doubt some fine maths :-))

But, is there say a connected 7x7 island with 3 tile_0's. This is what I meant in my previous post. Sorry, I may not have explained it too clearly.

The island can be any shape and contain as many tile_0's as required to 'pack it out' into a neat square or rectangle. A bit like your first island solution but with 1 more tile_0 and 1 less tile_255.

Thanks for the very quick solutions. They are quite neat. All connected I think is better. I just drew out your 'ASCII artwork' to help visualise them.

While you still have the old program out, I was wondering if there are any solutions which use every tile, except tile_0, just once? Because, if you create a set of puzzle tiles, you could produce just 46 tiles (not so prime and a bit cheaper than 47) which could be formed into a single island.

Or you could just have a seamless background of tile_0 and generate islands on top with just 46 tiles. I notice all solutions so far use duplicate tile_255's. Maybe this is necessary.

Very impressive. I love these computer 'brute force' solutions. Its amazing, I played around with a blob tileset for days but never found any of these neat layouts.

I drew out your 7x7 arrangement directly using the Stage tile explorer (on my cr31.co.uk website). The 2 blob brush tools need a bit of patience but do work. You can easily switch between different tilesets once drawn.

The tile index numbers are shown. Tile_0 does not have your central blob. I hope to design some more blob tilesets soon.

I'd be interested to know how many solutions there are. Is it hundreds or (as I suspect) just a few. Your new solution is composed of 2 islands. How many solutions retain a single land mass, or do any have more than 2 islands?

I appreciate such questions may not be easy to answer. But would be very interesting.

OK ... neat idea, I like the way the 2 different styles of tile_0 can be shown.

btw, you might be better using the following template. It has all 16 Wang tiles, but opposite edges match too! So you can tile a plain which allows you to check all possible edge combinations. It is the only 4x4 layout which does this (besides rotations and reflections). It's called Brigid's Cross. See my site http://www.cr31.co.uk/stagecast/wang/pattern.html for more technical info on using Wang tiles.

Yep - it could be fun There are real 3d mazes, usually made of wood, at some theme parks and places where you can wander around a physical layout. Problem is they can get boring for grown ups. Being 'in' a maze is quite a different experience than looking down on one.

Note: I've updated the above maze image, now includes better shadows. Also added the tileset to cr31 [Stage]. This is a Twin maze not a Blob maze. Select 'Brench' from the Twin Maze pull down menu to see random layouts.

You can extend Wang methods into 3D, using cubes instead of flat tiles. Cubes have 6 faces instead of a tiles 4 edges so you end up with 64 cubes in a complete ‘cubeset’. They should all fit together facelessly?? But you’ll need a 3D renderer to see the results - Unity web page plug in perhaps. All the extra complexity may not be worth the effort.

But certainly some of the tilesets could be recreated in a 3D game.

Maybe a maze generator plug-in for Minecraft is needed which can create ‘bridge over trench’ paths not just a flat ‘hedge maze’.

HiThursday, June 8, 2017 - 08:56Hi

Once the indices are calculated the job is done and all tile edges and corners should (in theory) match up !!

Not too sure I follow your 5_95_0_7 arrangement. This is the bottom left of a fixed tilemap layout. But see the explanation here (at my cr31 site) for generating random 'Blob' layouts by either Method 1 or Method 2.

The large random layout image is actually generated by a third Method 3. A simple orthogonal (no diagonals) maze is created and as the path progresses, rooms (or islands) are filled in. This ensures all rooms are connected. See here (bottom of page) for a fuller explanation.

An advantage of maze generation is that it can be adjusted to create a few long winding or many short stubby paths leading to different balance of rooms, paths and general meandering.

You can try it out here. Choose a Blob tileset and then click on 'Maze' (instead of 'Random') and watch it go to work. Mazes can be any size but the outer stage edge is always 0.

Also the generator never merges paths together (perfect maze only) so there is always one unique path between any two tiles. I might add in some further controls to allow for path merging.

Hope the links help. I'll tidy up some cr31 texts to make things clearer. Let me know if you need more info. Thanks, Guy.

Wow!! Yes - this is exactlySunday, May 29, 2016 - 11:00Wow!! Yes - this is exactly what I hoped existed.

I've drawn them out to better appreciate their beauty and (almost) perfect symmetry. It's the 'almost' that drives you potty when trying to find such layouts by hand.

So, a puzzle of 46 shaped pieces could be formed into a single connected island. Maybe into the 7 by 7 lid of the box the puzzle came in. A perfect Blob island.

Many thanks Caeles for your exhaustive searches and no doubt some fine maths :-))

All cool stuff.Thursday, May 19, 2016 - 14:30All cool stuff.

But, is there say a connected 7x7 island with 3 tile_0's. This is what I meant in my previous post. Sorry, I may not have explained it too clearly.

The island can be any shape and contain as many tile_0's as required to 'pack it out' into a neat square or rectangle. A bit like your first island solution but with 1 more tile_0 and 1 less tile_255.

Thanks for the very quickMonday, May 16, 2016 - 08:15Thanks for the very quick solutions. They are quite neat. All connected I think is better. I just drew out your 'ASCII artwork' to help visualise them.

While you still have the old program out, I was wondering if there are any solutions which use every tile,

excepttile_0, just once? Because, if you create a set of puzzle tiles, you could produce just 46 tiles (not so prime and a bit cheaper than 47) which could be formed into a single island.Or you could just have a seamless background of tile_0 and generate islands on top with just 46 tiles. I notice all solutions so far use duplicate tile_255's. Maybe this is necessary.

Hi caelesFriday, May 13, 2016 - 10:13Hi caeles

Very impressive. I love these computer 'brute force' solutions. Its amazing, I played around with a blob tileset for days but never found any of these neat layouts.

I drew out your 7x7 arrangement directly using the Stage tile explorer (on my cr31.co.uk website). The 2 blob brush tools need a bit of patience but do work. You can easily switch between different tilesets once drawn.

The tile index numbers are shown. Tile_0 does not have your central blob. I hope to design some more blob tilesets soon.

I'd be interested to know how many solutions there are. Is it hundreds or (as I suspect) just a few. Your new solution is composed of 2 islands. How many solutions retain a single land mass, or do any have more than 2 islands?

I appreciate such questions may not be easy to answer. But would be very interesting.

OK ... neat idea, I like theFriday, May 13, 2016 - 10:04Hi mawigator

OK ... neat idea, I like the way the 2 different styles of tile_0 can be shown.

btw, you might be better using the following template. It has all 16 Wang tiles, but opposite edges match too! So you can tile a plain which allows you to check all possible edge combinations. It is the only 4x4 layout which does this (besides rotations and reflections). It's called Brigid's Cross. See my site http://www.cr31.co.uk/stagecast/wang/pattern.html for more technical info on using Wang tiles.

Brilliant. Quite amazing. ITuesday, April 7, 2015 - 07:36Brilliant. Quite amazing. I’ll use these layouts for future Blob tile layout designs at cr31. Many thanks for your work.

Thanks for the shout. ITuesday, April 7, 2015 - 07:29Thanks for the shout. I really thought I had the minimum layout worked out. Quite amazing. I’ve updated the cr31 ‘Blob’ page and added a link to you.

Here is your 7x7 layout using the commune 'Blob' tileset:

Yep - it could be funThereThursday, June 12, 2014 - 09:17Yep - it could be fun

There are real 3d mazes, usually made of wood, at some theme parks and places where you can wander around a physical layout. Problem is they can get boring for grown ups. Being 'in' a maze is quite a different experience than looking down on one.

Note: I've updated the above maze image, now includes better shadows. Also added the tileset to cr31 [Stage]. This is a Twin maze not a Blob maze. Select 'Brench' from the Twin Maze pull down menu to see random layouts.You can extend Wang methodsThursday, June 12, 2014 - 08:59You can extend Wang methods into 3D, using cubes instead of flat tiles. Cubes have 6 faces instead of a tiles 4 edges so you end up with 64 cubes in a complete ‘cubeset’. They should all fit together facelessly?? But you’ll need a 3D renderer to see the results - Unity web page plug in perhaps. All the extra complexity may not be worth the effort.

But certainly some of the tilesets could be recreated in a 3D game.

Maybe a maze generator plug-in for Minecraft is needed which can create ‘bridge over trench’ paths not just a flat ‘hedge maze’.

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